A ribbon of length $5\frac{1}{4} \mathrm{m}$ is cut into small pieces each of length$\frac{3}{4} \mathrm{m}$. Find the number of pieces.

$\mathrm{Number} \mathrm{of} \mathrm{pieces}=\frac{\mathrm{Total} \mathrm{length} \mathrm{of} \mathrm{a} \mathrm{ribbon}}{\mathrm{Length} \mathrm{of} \mathrm{one} \mathrm{piece} \mathrm{of} \mathrm{ribbon}}$

$=\frac{5{\displaystyle \frac{1}{4}}}{{\displaystyle \frac{3}{4}}}$

$=5\frac{1}{4}÷\frac{3}{4}$

While dividing a mixed fraction by a fraction, first convert the mixed fraction into an improper fraction.

We have, $5\frac{1}{4}=\frac{21}{4}$

Therefore,

$5\frac{1}{4}÷\frac{3}{4}$

$=\frac{21}{4}÷\frac{3}{4}$

$=\frac{21}{4}\times \mathrm{reciprocal} \mathrm{of} \frac{3}{4}$

$=\frac{21}{4}\times \frac{4}{3}$

$=\frac{21\times 4}{4\times 3}$

$=\frac{21}{3}$

$=7$

Therefore, if a ribbon of length $5\frac{1}{4} \mathrm{m}$ is cut into small pieces each of length $\frac{3}{4} \mathrm{m}$ , the number of pieces will be 7.